Large-charge Rényi entropy

TL;DR

The paper computes the symmetry-resolved (charged) vacuum Rényi entropy $S_n(Q)$ for a disk in three-dimensional, strongly coupled CFTs at large global charge $Q$ using a large-charge EFT. Through a conformal map to a regulated hyperbolic space and a carefully defined UV regularisation, the authors show that the leading $O(1)$ contribution to $S_n(Q)$ is universal within the large-charge universality class and can be obtained from the one-particle spectrum around the large-charge saddle, independent of microscopic couplings. They provide explicit results for the $O(2)$ Wilson-Fisher CFT, including numerical spectra and the scaling of the charge fluctuation probability $p(Q) o e^{-Q^{3/2}}$, and present the leading $O(1)$ piece of $S_n(Q)$ with quantified coefficients $A_n$. The work demonstrates a concrete, holography-free computation of entanglement quantities in strongly-coupled CFTs and highlights the universality and potential broader applicability of the large-charge EFT in quantum information measures.

Abstract

The charged (symmetry-resolved) vacuum Rényi entanglement entropy on a disk is computed in the limit of large U(1) global charge for any Rényi index. We show that it behaves universally for a broad class of conformal field theories including the O(2) Wilson-Fisher fixed-point, by using the effective field theory at large global charge. The result establishes one of the first concrete computations of entanglement quantities in strongly-coupled field theories.

Figures (2)

• Figure 1: A plot of the large-charge von Neumann entropy $S_{n=1}^{(0)}(Q)$ in terms of $u_0$ (red dots) with a comparison to a fit (blue line). We see a perfect fit at large $e^{u_0}$.
• Figure 2: A plot of $A_n$ in terms of $n$ (red dots) with a comparison to a fit (blue line).